Theory of the earth's gravity field:
Saved in:
| Format: | Book |
|---|---|
| Language: | English Czech |
| Published: |
Amsterdam [u.a.]
Elsevier
1973
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus dem Tschech. übers. |
| Physical Description: | 538 S. Ill., graph. Darst. |
| ISBN: | 0444409394 |
Staff View
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| 245 | 1 | 0 | |a Theory of the earth's gravity field |c Miloš Pick ; Jan Pícha ; Vincenc Vyskočil |
| 264 | 1 | |a Amsterdam [u.a.] |b Elsevier |c 1973 | |
| 300 | |a 538 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Aus dem Tschech. übers. | ||
| 650 | 7 | |a Gravitation |2 obspm | |
| 650 | 4 | |a Gravité | |
| 650 | 7 | |a Terre |2 obspm | |
| 650 | 7 | |a Théorie générale |2 obspm | |
| 650 | 4 | |a Geodesy | |
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| 700 | 1 | |a Pícha, Jan |d 1917-1991 |e Sonstige |0 (DE-588)1036564428 |4 oth | |
| 700 | 1 | |a Vyskočil, Vincenc |e Sonstige |4 oth | |
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS
Contents 5
Preface 13
I Introduction
by Jan Picha
1 Gravimetry and Its Purpose 15
2 A Short History of Gravimetry 17
II Newton’s Theory of Potential
by Milos Pick
1 Introduction 19
2 Attraction of Point Masses 20
3 Volume Potential 20
4 The First Derivative of the Volume Potential 21
5 The Second Derivative of the Volume Potential 22
6 Gauss’s Formula 23
7 Volume Potential at Improper Points (Infinitely Distant) 24
8 Properties of the Volume Potential 25
9 Surface Potentials 25
10 Potential of a Double Layer 26
11 Continuity of the Potential of a Double Layer 27
12 The Normal Derivative of the Double-Layer Potential 29
13 Potential of a Single Layer 29
14 The Normal Derivative of the Potential of a Single Layer 30
15 Properties of the Potential of a Single and a Double Layer (Review of Results) 33
16 Potential of the Centrifugal Force 34
17 Chasles’s Theorem 35
*18 Physical Interpretation of Green’s Second Theorem 36
III Potential of Some Simple Formations, Approximate in Shape to the Figure of the Earth
by Milos Pick
1 Potential of a Homogeneous Spherical Layer and Its Derivatives 37
2 The Homogeneous Sphere 38
3 Potential of a Homogeneous Triaxial Ellipsoid and Its First Derivatives for an
Internal Point 39
6
4 First Derivatives of the Potential and the Potential of a Homogeneous Triaxial
Ellipsoid for an External Point 42
5 Potential of a Homogeneous Rotational Ellipsoid and Its First Derivatives 43
6 Potential of a Rotating Equipotential Rotational Ellipsoid Using the Solution of
the First Boundary Problem 45
7 Gravity of an Equipotential Ellipsoid 47
8 Equilibrium Bodies 50
9 An Ellipsoid as an Equilibrium Body 50
10 Maclaurin’s Ellipsoids 51
11 Jacobi’s Ellipsoids 53
12 The Relation Between the Maclaurin and Jacobi Ellipsoids 53
*13 Roche’s Model 55
14 Clairaut’s Problem 55
*15 Further Treatment of the Clairaut Theorem 56
16 Variation of the Attracting Force with Depth (Saigey’s Theorem) 57
17 Gravity Potential of a Rotating Body, Approximate in Shape to the Figure of the Earth 58
18 Clairaut’s Theorem 60
19 Gravity Potential of a Rotating Body 60
20 Normal Spheroids 63
21 Normal Gravity for Some Reference Ellipsoids 67
22 Potential of a Homogeneous Spheroid 68
*23 Convergence of Series for the Potential of a Triaxial Ellipsoid 69
*24 Development of the Potential Into a Series According to Wavre 70
25 Stokes’s Theorem 73
*26 Poincare’s Equation, Crudelli’s Conditions 74
IV Equipotential Surfaces Reductions
by Milos Pick
1 Equipotential Surfaces 77
2 Bruns’s Equation 80
3 The Plumb Line Curvature 81
4 Variation of Gravity on the Rotational Ellipsoid with Height Above Sea Level 84
5 Gravity Reduction in General 85
6 The Faye Reduction 87
7 The Bouguer Reduction 87
8 Computation of the Gravity Topographic Correction 89
9 Topographic Corrections Determination of the Effect of the Inner Region 93
10 The Rudzki Reduction 96
11 The Prey Reduction 98
12 Isostatic Reduction 98
13 The Graaff-Hunter Reduction (Model Earth) 101
14 Substitution of the External Gravity Field by the Potential of a Single Layer,
Spread Over the Surface of the Sea 102
15 Determination of the Figure of the Earth from the First Derivatives of the Gravity
Potential 104
16 Properties of the Disturbing Potential 108
7
V Absolute Gravity Measurements
by Jan Picha
1 Measurements of the Gravitational Constant 110
2 Absolute Measurements of the Acceleration of Gravity 113
VI Relative Measurements of the Acceleration of Gravity
by Jan Picha
1 Relative Gravity Measurements with Pendulum Instruments 120
1 1 Measurement of the Oscillation Period 121
1 2 Corrections of the Oscillation Period 124
a) Correction for the Clock Rate 124
b) Correction for the Effect of the Medium Surrounding the Pendulum
(Correction in Respect of Vacuum) 124
c) Temperature Corrections 126
d) Correction for an Infinitely Small Amplitude 128
e) Correction for the Co-oscillation of the Stand 130
f) Effect of the Pendulum Blade Camber 132
g) Effect of the Geomagnetic Field 134
1 3 Pendulum Instruments 136
2 Statical Methods of Relative Gravity Measurements 139
2 1 General Properties and the Theory of Gravimeters 139
a) Calibration of Gravimeter by Adding a Weight 147
b) Tilt Calibration 147
c) Calibration of Gravimeter by Measuring at Points with Known Values of
the Acceleration of Gravity 148
2 2 Description of Some Types of Gravimeters 148
a) Gravimeters with Metal Springs 149
b) Quartz Non-astatic Gravimeters 155
c) Quartz Astatic Gravimeters 160
d) On the Methods of Measuring with Static Gravimeters 163
2 3 Gravity Measurements at Sea 165
2 4 Gravity Measurements in Aircraft 168
2 5 Gravity Measurements Under Water and in Borholes 170
VII Measurements of the Second Derivatives of the Gravity Potential 171
by Jan Picha
VIII Some Comments on the Anomalous Gravity Field
by Vincenc Vyskocil
1 Definition of a Gravity Anomaly 179
2 Gravity Anomalies and the Investigation of the Structure of the Earth’s Crust 180
2 1 Gravity Anomalies Used in Applied Geophysics 180
2 2 On the Properties of Some Types of Anomalies 182
3 Graphical Representation of the Anomalous Gravity Field 185
4 Accuracy of Gravity Anomalies and of Gravity Maps 187
8
4 1 Accuracy of Gravity Anomalies at Observation Points 187
4 2 Theoretical Analysis of the Accuracy of Interpolated Values of Gravity
Anomalies 188
4 3 Accuracy of the Difference Between Gravity Anomalies at Two Points 191
4 4 Estimate of the Accuracy of a Gravity Map 192
IX Gravimetry and the Internal Structure of the Earth
by Vincenc Vyskocil
1 The Internal Structure of the Earth 195
2 Some Physical Properties of the Earth’s Body 197
2 1 Density Inside the Earth 197
2 2 Gravity, Pressure and Flattening of Equipotential Surfaces Inside the Earth 201
3 Density of Rocks of the Earth’s Crust 203
*3 1 Fundamental Terms 203
*3 2 Determination of Density by Weighing Rock Samples 204
*3 3 Density Derived from Gravity Measurements 206
*3 4 Densities of Most Common Rocks 209
4 The Earth’s Crust 212
5 Correlation Between Gravity Anomalies, Elevations Above Sea Level and Depths
of the Mohorovicic Discontinuity 214
5 1 Fundamental Terms 214
5 2 Correlation Between Gravity Anomalies Ag and Elevations h 217
5 3 Isostasy and Correlation Between Gravity Anomalies Ag, Elevations h and
Depths of the Mohorovicic Discontinuity H 219
6 General Principles of the Geological Interpretation of Gravity Anomalies 223
7 Application of the Gravimetric Method to Surveying Deposits of Usable Raw
Materials 224
X The Geoid
by Milos Pick
A The Geoid of a Regularized Earth 226
1 A Regularized Earth 226
2 Theory of the Regularized Geoid 228
3 Stokes’s Formula for an External Point 230
*4 Pizzetti’s Formula 233
*5 Stokes’s Forrqula for an External Point (cont ) 234
*6 Stokes’s Formula Derived by Solving the Third Boundary Problem 234
*7 Malkin’s Integral Equation 236
*8 Determination of the Height of the Geoid (Summary of Results) 237
*9 Idelson’s Integral Equation 239
*10 Molodenskii’s, Malkin’s and Monin’s Integral Equations 241
*11 Poincare’s Series 247
*12 Stokes’s Formula Without Using the Normal Gravity 248
*13 Determination of the Figure of the Geoid with an Accuracy to Small Quantities of
the First Order 251
*14 Limiting the Effect of the Influence of Distant Zones on the Height of the Geoid 252
*15 Potential and Mass of the Geoid 254
9
* 16 Practical Application of the Stokes’s Formula 255
17 Deviations of the Plumb Line 257
* 18 Vening Meinesz’s Formulae 258
19 Adjustment of Vening Meinesz’s Formulae for Near Zones 262
20 Practical Application of Vening Meinesz’s Formulae 264
21 Auxiliary Functions Necessary for Determining the Regularized Geoid 268
22 Determination of the Position of the Reference Body Relative to the Real Earth 271
*23 Influence of the Choice of the Normal Body on the Height of the Geoid and on the
Deviations of the Plumb Line 272
*24 Influence of the Choice of the Geodetic System on the Height of the Geoid and on
the Deviations of the Plumb Line 274
^ 25 The Mean Value of Normal Gravity 277
*26 The Figure of the Regularized Geoid Computed from Horizontal Gradients
of Gravity 279
27 Determination of the Mean Value of a Gravity Anomaly 280
1
B Theory of the Unregularized Geoid 282
28 The Unregularized Geoid 282
*29 Moiseev’s Determination of the Shape of the Unregularized Geoid 284
*30 Malkin’s Determination of the Shape of the Unregularized Geoid 286
*31 Molodenskii’s Determination of the Shape of the Unregularized Geoid 288
f *32 General Integral Equation for the Disturbing Potential of the Regularized and the
Unregularized Earth 289
XI Determination of the Figure of the Earth Without Considering Hypotheses About Its Internal
Composition
by Milos Pick
1 Determining the Figure of the Real Earth Generally 293
2 Heights Above Sea Level 294
*3 Molodenskii’s Quasigeoid 299
4 Solution of the Molodenskii’s Equation by Successive Approximations (Second
Method) 303
*5 Modification of the Molodenskii’s Method 308
*6 The Integro-differential Equation of Molodenskii for £ 309
! *7 The Linear Integral Equation for T 311
*8 The Mean Square Value of the Deflection of the Vertical for the Earth 312
*9 Computation of the Vertical Gradient of a Gravity Anomaly 313
*10 Bjerhammar’s Method 315
*11 Generalization of the Theory of Normal Heights 317
*12 Determination of the Figure of the Earth by Means of the Second Vertical Gra-
; dients of the Disturbing Potential 321
t
XII Time Variations of the Gravity Field
by Jan Plcha
t
1 Causes of Variations of Gravity with Time 323
2 Tidal Potential and Tidal Acceleration 325
*3 Static Tides on the Surface of an Absolutely Solid Earth 328
10
4 Oscillations of the Vertical Due to the Action of Tidal Forces on the Surface of an
Absolutely Solid Earth 331
5 Notation of Tidal Waves 336
XIII Observations of Tides of the Earth’s Crust
by Jan Picha
1 Introductory Comments and the Theory of the Horizontal Pendulum 338
1 1 Direct, Indirect and Secondary Effects Love’s Constants 343
2 Instruments for Tidal Measurements 345
2 1 The Quartz Horizontal Pendulum of Verbaandert and Melchior 345
2 2 The Photoelectric Ostrovskii Tiltmeter 346
2 3 The Lettau Horizontal Double Pendulum 348
2 4 The Vertical Pendulum for Tidal Measurements 348
3 Installation of Tiltmeter Sets 350
4 Measurements of Azimuths 352
5 Determination of the Sensitivity of Horizontal Pendula 358
6 Errors due to Instruments and to the Recording Equipment 366
7 Processing of Tidal Observations 369
XIV Fundamental Mathematical Principles of Gravimetric Interpretation
by Vincenc Vyskocil
1 General Comments 372
2 Separation of the “Regional” and “Local” Components of the Anomalous Gravity
Field 373
2 1 Review of Methods 373
2 2 The “Mean Value” Method 374
*2 3 Expression of the Regional Field by a Mathematically Definable Surface 375
*2 4 Transformation of the Anomalous Gravity Field to a Certain Height Above
the Earth’s Surface 376
*2 5 Stressing the Effect of Anomalous Masses at Small Depths by Means of the
Vertical Gravity Gradient 377
*2 6 The “Second Derivative” Method 378
2 7 Concluding Remarks 382
3 Initial Formulae for Gravimetric Interpretation 383
4 Direct and Inverse Gravimetric Problems for Simple Gravitating Bodies 387
41A Sphere 387
42A “Two-dimensional” Cylinder and a Material Straight Line 390
*4 3 “Two-dimensional” Prisms, Oblique and Vertical Steps 392
*4 4 An Infinitely Long, Horizontal, Material Plane Belt 395
*4 5 A Right Parallelepiped 398
5 Gravitating Bodies of Irregular Shape 400
5 1 The Direct Problem 400
5 2 Determination of the Total Mass and of the Coordinates of the Centre of
Mass of a Gravitating Body 402
*5 3 Estimate of the Depth of the Upper Boundary of a Gravitating Body 406
11
6 Shape of the Density Interface Determined from the Anomalous Gravity Field 410
6 1 Shape of the Interface Determined Along a Profile with Boreholes 410
6 2 Investigation of the Shape of the Bed of a Sedimentary Basin Without Refer-
ence Boreholes 411
6 3 Condensation of Anomalous Masses Bound to a Density Interface Into
a Horizontal Plane 411
7 Computation of Subsurface Anomalies (Analytical Continuation Downward) 414
7 1 Principle of the Method 414
7 2 Computation of a Subsurface Anomaly by Means of a Taylor Development 415
7 3 The Method of Finite Differences (Method of Nets) 416
*7 4 The Method of Computing Subsurface Anomalies by Means of a Development
Into a Fourier Series 417
*8 Shape of the Mohorovicic Discontinuity Determined from the Various Characte-
ristics of the Outer Gravity Field (by M Pick) 422
9 Some Comments on the Quantitative Interpretation of Gravity Anomalies 424
XV Substitution of the Earth’s Body by a Reference Surface
by Milos Pick
1 Representation of a Part of an Ellipsoid on Another by the Translation Method 425
2 Transformation from One Reference Surface to Another by Projection Along the
Normal to the Former Surface (Projection Method) 426
3 Longitudinal Distortion in the Projection Method 429
4 Deflections of the Vertical and the Laplace Equation 430
5 Relations Between Deflections of the Vertical and the Geographic Coordinates 434
6 Determination of Six Degrees of Freedom of a Reference Body 436
7 Transformation of Cartesian Coordinates into Geodetic Coordinates 437
XVI Astronomical and Astrogravimetric Levelling
by Milos Pick
1 Astronomical Levelling (a General Treatment) 439
2 Astrogravimetric Levelling (a General Treatment) 441
3 Molodenskii’s Astrogravimetric Levelling 443
4 Molodenskii’s Elliptical Transparency 447
5 Other Methods of Evaluating the Fundamental Equation of Astrogravimetric
Levelling 450
6 Astronomical and Astrogravimetric Levelling in Czechoslovakia 452
Appendix
by Milos Pick
1 Auxiliary Mathematical Relations 453
2 On Some Types of Improper Integrals 454
3 The r-function 455
4 Spherical Inversion of a Function 457
5 The Harmonic Function 458
6 Gauss’s Theorem 459
12
7 Gauss’s Integral 460
*8 Curvilinear Orthogonal Coordinate Systems in Space 461
*9 Molodenskii’s Operators 462
10 Laplace’s Expression 464
11 Green’s Theorem 466
12 Orthogonality of Functions 468
13 Spherical Functions 468
14 Series for the Function 1/r 470
15 Development of the Function Y(0, (p) Into a Series of Spherical Functions 471
*16 Solution of the Laplace’s Equation for a Sphere 472
*17 Sum of Series of Spherical Functions 473
18 Sums of Certain Series of Spherical Functions (Review of Results) 476
*19 Boundary Problems in General 479
*20 Green’s Function 480
*21 Properties of Green’s Function Gx 482
*22 Green’s Function for a Sphere 482
*23 Potential of an Inhomogeneous Spherical Layer 485
*24 Potential of an Inhomogeneous Spherical Double Layer 487
*25 Solution of the Dirichlet’s Problem for a Sphere Using Surface Integrals 488
*26 The Second Boundary Problem (Neumann’s Problem) 489
*27 Neumann’s Functions for a Sphere (Internal Problem) 491
*28 Neumann’s Function (External Problem) 493
*29 Solution of Neumann’s Problem for a Sphere Using Spherical Functions 493
*30 The Third Boundary Problem for a Sphere 495
*31 Integral Equations 496
*32 The Application of Integral Equations to the Solution of Boundary Problems
(Summary of Results) 498
References 501
Author Index 523
|
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| id | DE-604.BV007199017 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:57:29Z |
| institution | BVB |
| isbn | 0444409394 |
| language | English Czech |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-004606398 |
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| physical | 538 S. Ill., graph. Darst. |
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| publisher | Elsevier |
| record_format | marc |
| spelling | Theory of the earth's gravity field Miloš Pick ; Jan Pícha ; Vincenc Vyskočil Amsterdam [u.a.] Elsevier 1973 538 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Aus dem Tschech. übers. Gravitation obspm Gravité Terre obspm Théorie générale obspm Geodesy Gravity Erdmagnetisches Feld (DE-588)4191566-5 gnd rswk-swf Erdmagnetisches Feld (DE-588)4191566-5 s DE-604 Pick, Miloš 1926-2011 Sonstige (DE-588)121985296 oth Pícha, Jan 1917-1991 Sonstige (DE-588)1036564428 oth Vyskočil, Vincenc Sonstige oth HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004606398&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Theory of the earth's gravity field Gravitation obspm Gravité Terre obspm Théorie générale obspm Geodesy Gravity Erdmagnetisches Feld (DE-588)4191566-5 gnd |
| subject_GND | (DE-588)4191566-5 |
| title | Theory of the earth's gravity field |
| title_auth | Theory of the earth's gravity field |
| title_exact_search | Theory of the earth's gravity field |
| title_full | Theory of the earth's gravity field Miloš Pick ; Jan Pícha ; Vincenc Vyskočil |
| title_fullStr | Theory of the earth's gravity field Miloš Pick ; Jan Pícha ; Vincenc Vyskočil |
| title_full_unstemmed | Theory of the earth's gravity field Miloš Pick ; Jan Pícha ; Vincenc Vyskočil |
| title_short | Theory of the earth's gravity field |
| title_sort | theory of the earth s gravity field |
| topic | Gravitation obspm Gravité Terre obspm Théorie générale obspm Geodesy Gravity Erdmagnetisches Feld (DE-588)4191566-5 gnd |
| topic_facet | Gravitation Gravité Terre Théorie générale Geodesy Gravity Erdmagnetisches Feld |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004606398&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT pickmilos theoryoftheearthsgravityfield AT pichajan theoryoftheearthsgravityfield AT vyskocilvincenc theoryoftheearthsgravityfield |